1. Field of the Invention
The invention relates to a method for modeling stresses in the vicinity of a borehole and predicting the failure of liners or screens.
2. Background of the Invention
Sand control screens are utilized for various purposes in subterranean wells. The name derives from their early use in preventing the production of sand along with fluids from formations. A sand control screen is typically suspended from production tubing extending to the earth's surface and positioned in a wellbore opposite a productive formation. The wellbore in an annular area between the screen and the casing may be filled with a relatively large grain sand (“gravel”). This gravel prevents the fine sand from packing around the production tubing and screen and the screen prevents the large grain sand, gravel, from entering the production tubing. In this way, the sand control screen may exclude the produced sand while permitting the valuable fluids to enter the tubing for transport to the earth's surface. Perforated or slotted liners or expandable liners may also be used instead of a screen as a sand exclusion device. Hereafter, for the purposes of this application and the description of the invention, the term liner is used to refer to all such types of sand exclusion devices.
There are numerous prior art devices with different configurations of the liner and the components of the gravel pack and numerous methods for deployment of the devices. Examples of such devices are found in U.S. Pat. No. 5,829,522 to Ross et al., and U.S. Pat. No. 6,053,250 to Echols. Regardless of the device used and the method of deployment, the line and gravel pack must be designed to withstand the stresses in the subsurface formation: failure of the screen or a breakdown of the gravel pack can lead to sand production from the formation and plugging of the borehole. The selection and design of the liner depends on analysis of formation strength, strength distribution, permeability, permeability distribution, shale content, fines migration, and grain size and distribution. Of these factors, permeability, permeability distribution, grain size, and grain distribution can be measured with reasonable accuracy; however, most oil companies still have difficulty conducting formation strength and strength-distribution analyses. The two primary reasons for poor analysis are that mechanical logs available from service companies are not reliable or must be calibrated with other methods and that reasonably reliable numerical models for strength analysis are owned exclusively by several companies.
Another factor complicating the design of liners is that when fluid is produced from a reservoir, a reduction in pore pressure occurs. The pressure reduction is greater near the wellbore and increases with production time and rate. The reduction in pore pressure causes compaction of the formation containing the reservoir fluid, which imposes radial and axial loads on the well. Wellbore loads resulting from reservoir compaction are seldom considered in the design of casings, liners, and gravel-pack screens, yet they can be significant. Radial and axial pressures on wellbore tubulars from reservoir compaction are illustrated in FIG. 1 for a vertical well. For a deviated well, the wellbore is exposed to a radial component of the vertical overburden load, increasing external pressures on tubulars. Determining reservoir compaction loads on wellbore tubulars is not a simple task. Field measurement of reservoir compaction loads is difficult because of the time required for these loads to develop and the difficulty in measuring them. Simple analytic techniques for calculating reservoir compaction do not account for all the important variables affecting well loads. A computer model, however, can incorporate the many important variables to obtain realistic predictions of these loads.
Morita provides a comprehensive discussion of different sand-prediction models. As discussed therein, three types of field models are commonly used for predicting the onset of sand production. Core-based models are numerical models with a set of stress-strain curves as input to calculate the cavity stability and strength. Sonic based models are direct approximations from standard mechanical logs that calculate cavity stability using a linear stress/strain model. Regional statistical sand-production models involve back-calculation methods where a base solution incorporates a correction factor determined by field sand-production data.
Wooley & Prachner provide a methodology for the analysis of compaction loads on casings and liners of vertical and/or deviated boreholes resulting from reservoir depletion. The methodology uses a finite element simulation and is based on the separation of formation stress into a component of pore pressure and matrix stress. First, overall subsidence is computed with a large-scale model. The solution applies undisturbed boundary conditions far from the compacting reservoir and computes deformations and stresses near the well, in the reservoir, and in surrounding formations. Second, a near-well analysis is used to compute loads on the well. Effects of formations beyond the near-well region are transmitted to the solution by means of boundary displacements, which are defined from deformations computed with the large-scale model.
As discussed by Hamid et al., liner collapse occurs from application of differential pressures (across the screens) that exceed the collapse strength of the screen jacket. The resulting failure may not always be critical. In general, screen jacket collapse may lead to subsequent long term erosive failure.
Modeling of liner failure is typically carried out using a finite element analysis (FEA). Guinot et al. (U.S. Pat. No. 6,283,214) use a FEA to show that a particular shape and orientation of the perforations of a liner minimizes this destabilization, hence also minimizes sand production. In particular, and in the specific case of a vertical wellbore, for instance, elliptically shaped perforations, having the major axis aligned in the direction of maximum principal in situ, or compressive stress, improve the stability of the formation in the region near the wellbore, hence minimizing sand intrusion. Particularly preferred embodiments of this aspect of the Invention are perforations with an aspect ratio of about 5:1, and having their principal axis substantially aligned with the direction of maximum compressive stress.
Prior art methods of modeling the failure of liners predict the load on the liners using a combination of experimental data and FEA. The experimental data are used to define parameters of a model in which the parameters characterizing the liner and the formation are relatively uniform. There may be a variation in the stresses applied to the liner but the material comprising the liner and the formation is relatively homogenous. Failure prediction in models like this is based on average properties of the formation surrounding the liner as well as the liner itself. In reality, such homogeneity rarely exists in the formation around the well and in the liners: on a local scale, there may be statistical variations in the strength including anisotropy effects. In practice, failure usually occurs at the weakest point resulting in asymmetric loading creating localized deformation that can cause early failure of the liner. Accounting for statistical distribution of properties and the development of local failure areas are impractical to consider using the commonly used finite element analysis techniques. There is a need for a method of analysis and prediction of failure of liners that takes into account statistical variations in the properties of the vicinity of the borehole and liner. Such an invention should also be computationally fast. In addition, it is preferable that the invention should be user friendly in that specification of the material properties and loading be easily input and that the invention be able to provide graphical displays of the deformation and fracture process. The present invention satisfies this need.